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Cascade Correlation
Architecture and Learning Algorithm
for Neural Networks
Outline
 What is Cascade Correlation ?
 NN Terminology
 CC Architecture and learning Algorithm
 Advantages of CC
 References
What is Cascade Correlation ?
 Cascade-correlation (CC) is an architecture
and generative, feed-forward, supervised
learning algorithm for artificial neural
networks.
 Cascade-Correlation begins with a minimal
network, then automatically trains and adds
new hidden units one by one creating a
multi-layer structure.
NN Terminology
 An artificial neural network (ANN) is composed of
units and connections between the units. Units in
ANNs can be seen as analogous to neurons or
perhaps groups of neurons.
 Connection weights determine an organizational
topology for a network and allow units to send
activation to each other.
 Input units code the problem being presented to the
network.
 Output units code the network’s response to the
input problem.
NN Terminology
 Hidden units perform essential intermediate
computations.
 Input function is a linear component which
computes the weighted sum of the units input
values.
 Activation function is a non-linear component
which transforms the weighted sum in to final
output value
 In cascade-correlation, there are cross-connections
that bypass hidden units.
CC Architecture and learning
Algorithm
 Cascade-Correlation (CC) combines two ideas:


The first is the cascade architecture, in which hidden
units are added only one at a time and do not change
after they have been added.
The second is the learning algorithm, which creates and
installs the new hidden units. For each new hidden unit,
the algorithm tries to maximize the magnitude of the
correlation between the new unit's output and the residual
error signal of the network.
The Algorithm
1. CC starts with a minimal network consisting only
of an input and an output layer. Both layers are
fully connected.
2. Train all the connections ending at an output unit
with a usual learning algorithm until the error of
the net no longer decreases.
3. Generate the so-called candidate units. Every
candidate unit is connected with all input units
and with all existing hidden units. Between the
pool of candidate units and the output units there
are no weights.
The Algorithm
4. Try to maximize the correlation between the
activation of the candidate units and the residual
error of the net by training all the links leading to
a candidate unit. Learning takes place with an
ordinary learning algorithm. The training is
stopped when the correlation scores no longer
improves.
5. Choose the candidate unit with the maximum
correlation, freeze its incoming weights and add it
to the net.
The Algorithm
5. To change the candidate unit into a hidden
unit, generate links between the selected
unit and all the output units. Since the
weights leading to the new hidden unit are
frozen, a new permanent feature detector is
obtained. Loop back to step 2.
6. This algorithm is repeated until the overall
error of the net falls below a given value
A Neural Network trained with
Cascade Correlation Algorithm
Advantages of CC
 It learns at least 10 times faster than
standard Back-propagation Algorithms.
 The network determines its own size and
topologies.
 It is useful for incremental learning in which
new information is added to the already
trained network.
References
 The Cascade Correlation Learning
Architecture. Scott Fahlman and Christian
Lebiere.
 A Tutorial on Cascade-correlation. Thomas
R. Shultz